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Diffusive Shock Acceleration in Astrophysics
Athina Meli
Physics Department, National University of Athens
RICAP’07, 20-22 June, Rome
Cosmic Rays Observations
• Cosmic Rays are
subatomic particles and
radiation of extraterrestrial origin.
• First discovered in 1912 by
German scientist Victor
Hess, measuring radiation
levels aboard a balloon at
up to 17,500 feet (without
oxygen!)
• Hess found increased
radiation levels at higher
altitudes: named them
Cosmic Radiation
Cosmic Ray Spectrum – Key features…
10 decades of energy – 30 decades of flux !
E-2.7 ‘knee’  3x1015eV
 E-3.1 above the knee   1016eV
chemical transition 3x1018eV
 E-2.7 ‘ankle’   1018eV –1020eV
Transitions:1) nature of CR accelerators,
2) propagation
>6x1019 uncertainty (low flux, event st.)
GZK paradox….
dN
 E 
dE
Sources of cosmic ray acceleration
Requirements:
Magnetic field dimensions sufficient to contain
the accelerating particles.
Strong fields with large-scale structure
(astrophysical shocks)
E
max =  ·Z(B/1
Emax=
· B·G)
M(R/1 kpc)
ISM-SN: (Lagage&Cesarsky, 1983)
Wind-SN: (Biermann, 1993)
AGN radio-lobes: (Rachen&Biermann,1993)
AGN Jets or cocoon: (Norman et al.,1995)
GRB: (Meszaros&Rees, 1992,1994)
Neutron stars: (Bednarek&Protheroe,2002)
Pulsar wind shock: (Berezhko, 1994)
Hillas, 1984
1. Non-relativistic shocks in Supernovae
(ISM-SN & WIND-SN models)
Acceleration
observed in situ…
HESS collaboration: Aharonian et al
Nature 2004, 432, 75 – 77
Gamma-ray image
SNRSNR
RX RX
J0852.0-4622.
Gamma-ray
imageofofthethe
J1713.7 (G347).
Linear
of counts
Linearcolor
colorscale
scaleis isin units
in units
of counts.
The superimposed (linearly spaced) black contour
lines show the X-ray surface brightness as seen
by ASCA in the 1–3 keV range.
Relativistic Shocks: Shock speed approaches c (Vsk = u0 ~ c )
Main applications in:
1)
AGN Radio jets
2)
Gamma-Ray Bursts (fireball, internal shocks, afterglow)
More difficult to understand than non-relativistic shocks because:
•
Particle speed never >> shock speed. Cannot use diffusion approximation  No simple
test-particle power law derivable
•
Acceleration, even in test-particle limit, depends critically on scattering properties (i.e.,
self-gen. B-field), which are unknown
•
No direct observations of relativistic shocks. . .
•
PIC simulations more difficult to run
2. Active Galactic Nuclei (AGN)
Central engine accretion disks, jets
and hot spots
3C219
3. Gamma Ray Bursts
What‘s a GRB?
Fermi acceleration
• Second order Fermi acceleration (Fermi, 1949)
• First order Fermi acceleration -diffusive acceleration- (Krymskii, 1977; Bell,
1978a,b; Blandford&Ostriker, 1978; Axford et al. 1978)
Transfer of the macroscopic kinetic energy of
moving magnetized plasma to individual charged
particles  non- thermal distribution
Second order Fermi acceleration
• Particles are reflected by ‘magnetic mirrors’
associated with irregularities in the galactic
magnetic field. Net energy gain.
• Cloud frame:
1) No change in energy
(colissionless scattering, elastic)
2) Cosmic ray’s direction randomised
• If particles remain in the acceleration region
for   power law distribution :
N(E)  E-
=1+1/ and   (V/c)2
The average energy gain per collision:
<E/E> = (V/c)2
First order Fermi acceleration
(diffusive shock acceleration)
1970’s modification of general theory: Particles
undergo a process on crossing a shock
from upstream to downstream and back again
(Supernovae shocks)

V1

V2
Power-law distribution depends only on
compression ratio, r :
N(E)  E-
=(r+2)/(r-1), r=V1/V2 =(+1)/ ( -1)
for mono-atomic gas =5/3  r=4  E-2
The average energy gain per collision:
<E/E> = V/c
Note: Only for non-relativistic shocks
upstream
downstream
Sub-luminal and super-luminal relativistic shocks

The Lorentz transformation is limited due to VHT V1 tany1
Relativistic shocks?  Monte Carlo simulation technique
Analytical solutions Vs Numerical Simulations
• Notion of ‘test particles’  interact with the plasma shock waves but do
not react back to modify the plasma flow.
• Very efficient in describing particle ‘random walks’.
• Random number generation simulation of the random nature of a physical
process.
• Follow closely each particle path using a large number of particles.
• Apply escape (momentum and spatial) boundaries in the simulation box,
according to certain physical conditions.
• Does the Fermi acceleration mechanism hold at relativistic speeds
(universality?)
• Are different models of particle diffusion important?
• What is the energy gain efficiency per shock cycle?
• How the spectra look like at the source of the acceleration?
• Is the acceleration faster in relativistic shocks?
• . . . What else . . .?
1. Relativisitic sub-luminal shocks
O
O
Spectral shape for upstream gamma
equal to 10 and magnetic field inclination
at 35 degrees. Later we will
observe the smoothness of the spectral
shape compared to larger upstream gammas.
Spectral shape for gamma=500. Top plots: shock at 15o, r = 3,4. Bottom plots:
shock at 35o, r = 3,4 respectively.
Spectral shapes for an upstream gamma = 300
Niemiec & Ostrowski 2004
Spectrum depends on how particles scatter. Here, Niemiec & Ostrowski calculate
particle trajectories in various magnetic field configurations, F(k).
-Spectrum not necessarily a power law
-Cutoffs if no magnetic turbulence at relevant scales
Note: Acceleration in relativistic shocks depends critically on details of diffusion and
details of diffusion are unknown
The angular distribution of the logarithm of the number of the transmitted particles versus mu= cos. Top
plots: Gamma=200, at 15o. Bottom plots: Gamma=1000, at 35o. Strong ‘beaming ’ (Lieu and Quenby, 1993).
The ratio of the computational
time to the theoretical acceleration time
constant. Top at 15o, bottom at 35o.
2. Efficiency of Fermi acceleration at relativistic super-luminal shocks
pitch angle diffusion
large angle scattering
Spectra for Gamma=300 and angle of 76 degrees. Left, pitch angle diffusion. Right, same values
for large angle scattering. Note: in this case there is no ‘structure’ in the spectrum.
pitch angle diffusion
Left, shock lorentz factor of 500 and angle of 76 degrees. Right, shock lorentz of 900
and shock inclination angle of 89 degrees.
Findings
•
Spectral shape  scatter model (details of diffusion)
•
•
•
•
Highly anisotropic angular distribution (‘beaming effect’)
‘Speed-up’ effect (faster acceleration)
Gamma squared energy boosting (first cycle)
Sub-luminal shocks more efficient then Super-luminal
0  a 1
The energy density of the observed cosmic ray spectrum
JE is then used to normalise the calculated Monte Carlo
spectra
The diffuse energy spectrum of sources, compared
to the total diffuse spectrum (Meli, Becker & Quenby (‘06 ’07))
Conclusions
Non-Relativistic shocks:
First-order Fermi acceleration mechanism (Diffusive shock acceleration) it is well
studied  predictions for spectral shapes from earth’s bow shock, planetary
shocks and Supernova Remnants it works.
Relativistic Shocks :
•
•
•
Important in AGN radio jets and GRBs
•
Application to GRBs and AGN – still work to be done…
Diffusive shock acceleration harder to describe (but still seems to work)
Spectrum depends on (1) unknown scattering properties, (2) shock Lorentz
factor, (3) obliquity  “Universal” power law index, f(p)  p-4.2 is a special case
Thank you